A compact and efficient algorithm for digital envelope detection in white light interferograms is derived from a well-known phase-shifting algorithm. The performance of the new algorithm is compared with that of other schemes currently used. Principal criteria considered are computational efficiency and accuracy in the presence of miscalibration. The new algorithm is shown to be near optimal in terms of computational efficiency and can be represented as a second-order nonlinear filter. In combination with a carefully designed peak detection method the algorithm exhibits exceptionally good performance on simulated interferograms.

https://nontrivialzeros.net/KGL_Papers/23_Neat_Algorithm_JOSAA96.pdf

Efficient nonlinear algorithm for envelope detection in white light interferometry

A simple expression is given for evaluating the effective or average radius of curvature R(z) of an arbitrarily wrinkled, distorted, or nondiffraction-limited optical beam. This real-beam radius of curvature obeys the same free-space propagation equation as does the wavefront curvature of an ideal Gaussian beam. Extracting this correctable curvature from the beam at any plane simultaneously collimates the beam, makes that location a waist for the real beam, and minimizes the far-field beam divergence starting from that position. >

Defining the effective radius of curvature for a nonideal optical beam

A method and apparatus for determining the quality of a multimode laser beam (10). In the preferred embodiment, the apparatus includes a lens (32) for creating a transformed or imaged waist from the input beam. The location of the transformed beam waist and its diameter are then determined. These steps can be carried out by chopping the beam using a rotating hub (34) having apertures (36,38) for selectively passing the beam. Preferably, one of the apertures has a pair of 45° knife edges (40,42). The transmission of the beam past the knife edge is monitored by a detector (30). In operation, the lens focal position is varied while the transmission of the beam past the knife edge is monitored in order to locate and measure the diameter of the transformed waist. The diameter of the beam at one other known location is measured. A processor then calculates beam quality by fitting these measurements to a mathematical model. Once the quality of the beam is calculated, the location of the original beam waist and its diameter can be derived. Once all of the beam parameters are derived, the propagation characteristics of the beam can be predicted.

Apparatus for measuring the mode quality of a laser beam

A dispersive model for the propagation of ultrasound in soft tissue

The focal shift for a lens of finite value of Fresnel number can be defined in terms of the second moment of the intensity distribution in transverse planes. The connection with the optical transfer function is described. The specification of the focused amplitude in terms of the fractional Fourier transform is discussed, and the connections among the fractional Fourier transform, the Wigner distribution, and the ambiguity function are described, leading to a model for effects of Fresnel number in terms of a rotation in phase space. The uncertainty principle is discussed, including the significance of the beam propagation factor M 2 and the width of optical fiber beam modes. Calculation of the moments in terms of the modulus and the phase of the illuminating wave is presented, and the use of the Kaiser‐Teager energy operator is also described. © 2000 Optical Society of America [S0740-3232(00)00404-X] OCIS codes: 060.2270, 070.2580, 070.2590, 140.3300, 260.1960.

http://nontrivialzeros.net/KGL_Papers/35_Focal_shift_JOSA_2000.pdf

Focal shift, optical transfer function, and phase-space representations

Using the variance measure of duration, it is shown that the duration of a signal is composed of two terms. The first term is the duration of the zero-phase equivalent signal, and the second term is the variance of the phase derivative of the Fourier transformed signal.

S.C. Pohlig

Papers

Signal duration and the Fourier transform